A detonation is a combustion-driven shock wave. Typically, a detonation will consist of an inert shock followed by a region of chemical reaction referred to as the reaction zone. Detonations have a wide variety of engineering applications, from obvious military uses to explosive welding, hard rock mining, and materials processing. Detonations can occur in a variety of materials, including gases (such as premixed hydrogen and oxygen), liquids, and solid explosives. Of particular interest in detonation problems is the motion of the detonation shock. Changes to the reaction zone may cause large variations in the strength and speed of the detonation front, so it can not be ignored in modeling detonations. For typical explosives, the reaction zone may be thousands of times smaller than the engineering scale. This multi-scaled nature of detonation can pose problems when trying to predict the motion of the detonation front.Detonation shock dynamics is an asymptotic theory whose key result is an intrinsic partial differential equation for the dynamics of the detonation shock front. It will be demonstrated that the theory can predict several aspects of unsteady multi-dimensional detonations accurately. Three intrinsic relations will be examined and compared with direct numerical simulations. Their relevance to modeling detonation dynamics will also be given. Numerical methods, based on level-set ideas, will be given for propagating multi-dimensional detonation fronts in arbitrarily complex geometries.